I have several time series. Series 1 might have an average of 55, series 2 might have an average of 20, and so on. Each series sticks close to its average.
Occasionally, the value of a series will change significantly (wrt the average). Maybe from 55 to 115, for example. Sometimes the value in the adjacent series (series 2, for the case of series 1) will change significantly (wrt its average) at the same time. Sometimes it won't.
I'm looking for a way to determine when adjacent series tend to change at the same time. I'm not worried about the numbers (55 to 115, 20 to x), but rather I'm looking to determine if they tend to change at the same time. Two adjacent series will either change at the same time always (they're related), or not very often (due to just chance).
What's a good tool for this?
The concepts you are looking for are called cross-correlation and cross-covariance.